Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focusing on the behavior of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area and volume-law entanglement, being characteristic of the quantum disentangled liquid. This behavior appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.A. S. acknowledges EPSRC for studentship funding under Grant No. EP/M508007/1. J. K. is supported by the Marie Curie Programme under EC Grant agreement No. 703697. The work of D. L. K. was supported by EPSRC Grant No. EP/M007928/1. R. M. was in part supported by DFG under Grant No. SFB 1143

Majorana spectroscopy of three-dimensional Kitaev spin liquids

We analyse the dynamical response of a range of 3D Kitaev quantum spin-liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines or Weyl points. We find that the behaviour of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a non-vanishing density of states, to the phase shifts encountered in the corresponding X-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine-structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalise, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations.The collaboration was supported by the Helmholtz Virtual Institute “New States of Matter and their Excitations” and the German Science Foundation under SFB 1143. The work of J.K. is supported by a Fellowship within the Postdoc-Program of the German Academic Exchange Service (DAAD). A.S. would like to acknowledge the EPSRC for studentship funding under Grant No. EP/M508007/1. J.T.C. is supported by EPSRC Grant No. EP/I032487/1, D.K. is supported by EPSRC Grant No. EP/M007928/1.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the American Physical Society

Dynamical localization in Z(2) lattice gauge theories

We study quantum quenches in two-dimensional lattice gauge theories with fermions coupled to dynamical Z2 gauge fields. Through the identification of an extensive set of conserved quantities, we propose a generic mechanism of charge localization in the absence of quenched disorder both in the Hamiltonian and in the initial states. We provide diagnostics of this localization through a set of experimentally relevant dynamical measures, entanglement measures, as well as spectral properties of the model. One of the defining features of the models that we study is a binary nature of emergent disorder, related to Z2 degrees of freedom. This results in a qualitatively different behavior in the strong disorder limit compared to typically studied models of localization. For example, it gives rise to a possibility of a delocalization transition via a mechanism of quantum percolation in dimensions higher than 1D. We highlight the importance of our general phenomenology to questions related to dynamics of defects in Kitaev's toric code, and to quantum quenches in Hubbard models. While the simplest models we consider are effectively noninteracting, we also include interactions leading to many-body localizationlike logarithmic entanglement growth. Finally, we consider effects of interactions that generate dynamics for conserved charges, which gives rise to only transient localization behavior, or quasi-many-body localization

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet.

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl3, continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin-orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl3 as a prime candidate for fractionalized Kitaev physics.Research using ORNL’s HFIR and SNS facilities was sponsored by the US Department of Energy, Office of Science, Basic Energy Sciences (BES), Scientific User Facilities Division. A part of the synthesis and the bulk characterization performed at ORNL was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division (C.A.B. and J.-Q.Y.). The work at University of Tennessee was funded in part by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4416 (D.G.M. and L.L.). The work at Dresden was in part supported by DFG grant SFB 1143 (J.K. and R.M.), and by a fellowship within the Postdoc-Program of the German Academic Exchange Service (DAAD) (J.K.). D.L.K. is supported by EPSRC Grant No. EP/M007928/1. The collaboration as a whole was supported by the Helmholtz Virtual Institute ‘New States of Matter and their Excitations’ initiative.This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nmat460

Exact form of the Bogoliubov excitations in one-dimensional nonlinear Schrödinger equation

In this Letter we present the exact solutions of one-dimensional nonlinear Schrödinger equation. The solutions correspond to the Bogoliubov excitations in Bose-gas with a local interaction. The obtained expression is used for evaluating the transmission coefficient of the excitations across a δ-functional potential barrier

Quantized gravitational responses, the sign problem, and quantum complexity

It is believed that not all quantum systems can be simulated efficiently using classical computational resources. This notion is supported by the fact that it is not known how to express the partition function in a sign-free manner in quantum Monte Carlo (QMC) simulations for a large number of important problems. The answer to the question-whether there is a fundamental obstruction to such a sign-free representation in generic quantum systems-remains unclear. Focusing on systems with bosonic degrees of freedom, we show that quantized gravitational responses appear as obstructions to local sign-free QMC. In condensed matter physics settings, these responses, such as thermal Hall conductance, are associated with fractional quantum Hall effects. We show that similar arguments also hold in the case of spontaneously broken time-reversal (TR) symmetry such as in the chiral phase of a perturbed quantum Kagome antiferromagnet. The connection between quantized gravitational responses and the sign problem is also manifested in certain vertex models, where TR symmetry is preserved

Quantized gravitational responses, the sign problem, and quantum complexity

It is believed that not all quantum systems can be simulated efficiently using classical computational resources. This notion is supported by the fact that it is not known how to express the partition function in a sign-free manner in quantum Monte Carlo (QMC) simulations for a large number of important problems. The answer to the question-whether there is a fundamental obstruction to such a sign-free representation in generic quantum systems-remains unclear. Focusing on systems with bosonic degrees of freedom, we show that quantized gravitational responses appear as obstructions to local sign-free QMC. In condensed matter physics settings, these responses, such as thermal Hall conductance, are associated with fractional quantum Hall effects. We show that similar arguments also hold in the case of spontaneously broken time-reversal (TR) symmetry such as in the chiral phase of a perturbed quantum Kagome antiferromagnet. The connection between quantized gravitational responses and the sign problem is also manifested in certain vertex models, where TR symmetry is preserved

Multicomponent Skyrmion lattices and their excitations

We study quantum Hall ferromagnets with a finite density of topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrized by a d -component spinor field. In the absence of anisotropies we find a hexagonal Skyrmion lattice that completely breaks the underlying SU(d) symmetry with the low-lying excitation spectrum separating into d2−1 gapless acoustic magnetic modes and a magnetophonon. The ground state charge density modulations, which inevitably exist in these lattices, vanish exponentially in d. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant to experiments with AlAs quantum wells. Here we find a transition which breaks a sixfold rotational symmetry of the triangular lattice, followed by the formation of a square lattice at large values of anisotropy strength

Bulk-edge correspondence in fractional Chern insulators

It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems—fractional Chern insulators and the fractional quantum Hall states—via generalization of a gauge-fixed Wannier-Qi construction in the cylinder geometry. Our setup offers a number of important advantages compared to the earlier exact diagonalization studies on a torus. Most notably, it gives access to edge states and to a single-cut orbital entanglement spectrum, hence to the physics of bulk-edge correspondence. It is also readily implemented in the state-of-the-art density matrix renormalization group method that allows for numerical simulations of significantly larger systems. We demonstrate our general approach on examples of flat-band models on ruby and kagome lattices at bosonic filling fractions ν = 1/2 and ν = 1, which show the signatures of (non)-Abelian phases, and establish the correspondence between the physics of edge states and the entanglement in the bulk. Notably, we find that the non-Abelian ν = 1 phase can be stabilized by purely on-site interactions in the presence of a confining potential

Bose-Einstein condensation of magnons in Cs2CuCl4: A dilute gas limit near the saturation magnetic field

Based on the realistic spin Hamiltonian for the frustrated quasi-two-dimensional spin-1∕2 antiferromagnet Cs2CuCl4, a three-dimensional spin ordering in the applied magnetic field B near the saturation value Bc is studied within the magnon Bose-Einstein condensation scenario. Using a hard-core boson formulation of the spin model, a strongly anisotropic magnon dispersion in Cs2CuCl4 is calculated. In the dilute magnon limit near Bc, the hard-core boson constraint results in an effective magnon interaction which is treated in the Hartree-Fock approximation. The critical temperature Tc is calculated as a function of the magnetic field B and compared with the phase boundary Tc(B) experimentally determined in Cs2CuCl